The author investigates the possibility of the build-up of ion-cyclotron perturbations in an inhomogeneous plasma having a finite ratio between its pressure and the pressure of a magnetic field. It is shown that the plasma is more stable with respect to such perturbations at finite pressure than at zero pressure. The stabilization is associated with a smearing of the cyclotron resonance resulting from the velocity dependence of the magnetic drift of the ions; it is also linked with Landau damping in the electrons, the magnetic drift of which coincides with the wave phase velocity.